Michael is 40 years older than Ashley. Eight years ago, Michael was 5 times as old as Ashley. How old is Ashley now?
Solution: We can use the given information to write down two equations that describe the ages of Michael and Ashley. Let Michael's current age be $m$ and Ashley's current age be $a$ The information in the first sentence can be expressed in the following equation: $m = a + 40$ Eight years ago, Michael was $m - 8$ years old, and Ashley was $a - 8$ years old. The information in the second sentence can be expressed in the following equation: $m - 8 = 5(a - 8)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $a$ , it might be easiest to use our first equation for $m$ and substitute it into our second equation. Our first equation is: $m = a + 40$ . Substituting this into our second equation, we get the equation: $(a + 40)$ $-$ $8 = 5(a - 8)$ which combines the information about $a$ from both of our original equations. Simplifying both sides of this equation, we get: $a + 32 = 5 a - 40$ Solving for $a$ , we get: $4 a = 72$ $a = 18$.